Are prices centrally decided in Marxism?
If so are they based on labour value?
I'm not sure if you are asking about theoretical Marxism as espoused by Marx himself (this is covered in detail in Labor Theory of Value Wikipedia page, no need to elaborate here), or in Marxism-derived socioeconomic systems like USSR. Since Wikipedia answered the former, I will address the latter.
Libertarianism.com well-referenced article "A World without Prices: Economic Calculation in the Soviet Union" explained at high level how Soviet economy worked, at both production level, wage level, and retail price level. On the last one:
Prices of retail goods were determined in a similar fashion (to wages and production). Gosplan, knowing the total amount of money going towards wages (described earlier in the article) and therefore the amount of money available for consumption, would take that amount and set it equal to the value of all the goods that were to be produced that year according to their plan. From there, Gosplan could set the price of every good, again typically relying on the labor theory of value, the sum total of which would add up to the total of workers’ wages. In this way, Gosplan kept rigid prices that ideally reflected the value of the labor required to produce it. Again, all transactions went through Gosbank.
Obviously, Gosplan being Gosplan, if you discount black market economy, the prices were indeed set centrally.
Not really - Marxism is not a way to run the economy or society. To quote wikipedia: "Marxism is a method of socioeconomic analysis". I think it is a very common mistake to identify Marxism with later attempts at constructing ideologies based on this analysis; allegedly he wasn't himself all that impressed with the results - he is supposed to have said something like "If that is Marxism, then I am not a Marxist".
There are at least three reasons why prices aren't centrally-fixed and why you can't artificially increase the value of your shoes by spending more time producing them:
Although some countries using Marx's name have used central planning to determine prices, Marx himself did not advocate this idea. Marxist theory (starting at least with Friedrich Engels, though he attributed the idea to Marx himself) predicted that the communist world would not have a state. Without class antagonism it would wither away and die in obscurity.
Without a state, it isn't clear who would set prices.
Wikipedia has a summary of this idea here.
If you can find access, a fine article was published in the Journal of the History of Ideas here. That article pursues different dimensions of the withering away of the state. In particular, after the state is gone some minimal administrative organ may remain. What exactly this is supposed to be isn't clarified in Marx's work.
Marx differentiated between two forms of value: exchange value and use value [short write-up from Iowa State University here].
Use value is based on how useful something is. Your theoretical shoes have use value based on their durability, size, and other features. In some sense, this is the "true" usefulness of a thing, regardless what the price at market was.
Exchange value is the value something has on a market, as determined by the buyer and seller. Marx was critical of exchange value, because it is a distorts the value of a thing. He observed that exchange value is often more than the use value, and the extra value (in the form of profits) are retained by bourgeoisie, creating a kind of feedback loop of repression: the bourgeoisie extract value from the workers, and then use their fictional extra value to enhance their ability to extract value from workers.
It also distorts values in the opposite direction: when the exchange value is below the use value, the item is not produced (or under-produced) in capitalism, because no firm would spend the money to produce something they couldn't sell for more.
In communism, surplus value is minimized: the market price of goods is similar to their use value. The mechanism here is really marketing: under capitalism goods are produced for the bourgeoisie based on the surplus value that can be extracted. Without the need to generate profits for the bourgeoisie, the two values are the same.
In your case, no matter how much labor your shoes took to create, their value will only ever be their use-value.
Marx also differentiated between a commodity and product. Commodities are traded on a market, while products are not.
If you spend twice as much labor producing a pair of shoes than is necessary for its features, than you aren't going to be able to trade it at the price that it's labor suggests. No one would take that offer, and your labor will have amounted to nothing.
You will have to settle for the price of other shoes with the same features, even though they took less labor to produce. In this case, you probably over-estimated the value of your own labor. You added additional labor, but didn't realize additional use-value as you did so.
Now, if your shoes fill some need in society, that extra labor may be justified and you can get the price you want. But that's because those shoes have additional use-value, not because of the labor exerted on them.
These two quotes from Marx describe the different between products and commodities. Read more in the same section to get some of his ideas on markets, surplus value, and labor:
To produce a commodity a certain amount of labour must be bestowed upon it, or worked up in it. And I say not only labour, but social labour. A man who produces an article for his own immediate use, to consume it himself, creates a product, but not a commodity. As a self-sustaining producer he has nothing to do with society.
But to produce a commodity, a man must not only produce an article satisfying some social want, but his labour itself must form part and parcel of the total sum of labour expended by society. It must be subordinate to the division of labour within society. It is nothing without the other divisions of labour, and on its part is required to integrate them.
[Source: Value, Price, and Profit]